Database of Modular Polynomials

class sage.databases.db_modular_polynomials.AtkinModularCorrespondenceDatabase

Bases: ModularCorrespondenceDatabase

model = 'AtkCrr'

class sage.databases.db_modular_polynomials.AtkinModularPolynomialDatabase

Bases: ModularPolynomialDatabase

The database of modular polynomials Phi(x,j) for \(X_0(p)\), where x is a function on invariant under the Atkin-Lehner invariant, with pole of minimal order at infinity.

model = 'Atk'

class sage.databases.db_modular_polynomials.ClassicalModularPolynomialDatabase

Bases: ModularPolynomialDatabase

The database of classical modular polynomials, i.e. the polynomials Phi_N(X,Y) relating the j-functions j(q) and j(q^N).

model = 'Cls'

class sage.databases.db_modular_polynomials.DedekindEtaModularCorrespondenceDatabase

Bases: ModularCorrespondenceDatabase

The database of modular correspondences in \(X_0(p) \times X_0(p)\), where the model of the curves \(X_0(p) = \Bold{P}^1\) are specified by quotients of Dedekind’s eta function.

model = 'EtaCrr'

class sage.databases.db_modular_polynomials.DedekindEtaModularPolynomialDatabase

Bases: ModularPolynomialDatabase

The database of modular polynomials Phi_N(X,Y) relating a quotient of Dedekind eta functions, well-defined on X_0(N), relating x(q) and the j-function j(q).

model = 'Eta'

class sage.databases.db_modular_polynomials.ModularCorrespondenceDatabase

Bases: ModularPolynomialDatabase

class sage.databases.db_modular_polynomials.ModularPolynomialDatabase

Bases: object